i

MODELLING EFFECTS OF INSUFFICIENT LAP SPLICES ON A DEFICIENT REINFORCED

CONCRETE FRAME

A THESIS SUBMITTED TO

THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES

OF

MIDDLE EAST TECHNICAL UNIVERSITY

BY

WESLEY WEI-CHIH LIN

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR

THE DEGREE OF MASTER OF SCIENCE

IN

EARTHQUAKE ENGINEERING AND ENGINEERING SEISMOLOGY

JANUARY 2013

ii

Approval of the thesis:

MODELLING EFFECTS OF INSUFFICIENT LAP SPLICES ON A

DEFICIENT REINFORCED CONCRETE FRAME

submitted by WESLEY WEI-CHIH LIN in partial fulfillment of the requirements

for the degree of Master of Science in Earthquake Engineering and Engineering

Seismology, Middle East Technical University by,

Prof. Dr. Canan Özgen ___________________

Dean, Graduate School of Natural and Applied Sciences

Prof. Dr. Ahmet Cevdet Yalçıner ___________________

Head of Department, Civil Engineering

Prof. Dr. Haluk Sucuoğlu ___________________

Supervisor, Civil Engineering Dept., METU

Prof. Dr. Barış Binici ___________________

Co-Supervisor, Civil Engineering Dept., METU

Examining Committee Members:

Prof. Dr. Güney Özcebe ___________________

Civil Engineering Dept., METU

Prof. Dr. Haluk Sucuoğlu ___________________

Civil Engineering Dept., METU

Prof. Dr. Ahmet Yakut ___________________

Civil Engineering Dept., METU

Assoc. Prof. Dr. Erdem Canbay ___________________

Civil Engineering Dept., METU

Asst. Prof. Dr. Tahsin Turgay ___________________

Architecture Dept., Abant İzzet Baysal University

Date: 29.01.2013aaaaa

iii

I hereby declare that all information in this document has been obtained and presented in

accordance with academic rules and ethical conduct. I also declare that, as required by these

rules and conduct, I have fully cited and referenced all material and results that are not original

to this work.

Name, Last name: Wesley Wei-Chih Lin

Signature : __________________

iv

ABSTRACT

MODELLING EFFECTS OF INSUFFICIENT LAP SPLICES ON A DEFICIENT

REINFORCED CONCRETE FRAME

Lin, Wesley Wei-Chih

M.Sc., Department of Civil Engineering

Supervisor: Prof. Dr. Haluk Sucuoğlu

Co-Supervisor: Prof. Dr. Barış Binici

January 2013, 63 pages

In order to reduce seismic risk in vulnerable buildings, buildings identified to be at risk should be

assessed and strengthened. Performance evaluation of deficient buildings has become a major concern

due to devastating earthquakes in the past. In order to justify new provisions in design and assessment

codes, experiments and analyses are inherently necessary.

In this thesis study, investigations into the behaviour of two deficient reinforced concrete frames built

at Middle East Technical University’s Structural and Earthquake Laboratory and tested via pseudo-

dynamic tests were made. These frames were modelled on the OpenSees platform by following

methods of analyses outlined in the Turkish Earthquake Code of 2007 (TEC 2007) and ASCE/SEI-

41-06. Both deficient frames were essentially the same, with the only difference being the presence of

insufficient lap splices, which was the focus of the study.

Time history performance assessments were conducted in accordance to TEC 2007’s damage state

limits and ASCE/SEI 41-06’s performance limits. The damages observed matched the performance

levels estimated through the procedure outlined in TEC 2007 rather well. Specific to the specimen

with lap splice deficiencies, ASCE/SEI 41-06 was overly conservative in its assessments.

TEC 2007’s requirements for lap splice lengths were found to be conservative in the laboratory and

are able to tolerate deficiencies up to 25% of the required length.

With respect to mathematical models, accounting for materials in deficient systems by using nominal

but reduced strength properties is not very efficient and unless joint deformations are explicitly

accounted for, local deformations cannot be captured.

Keywords: Pseudo-Dynamic Testing, Numerical Simulations, Performance Evaluations, Lap Splice

Deficiencies

v

ÖZ

YÖNETMELİĞE UYGUN OLMAYAN BETONARME ÇERÇEVEDE YETERSİZ

BİNDİRMELİ EKLERİN MODELLEMEDEKİ ETKİLERİ

Lin, Wesley Wei-Chih

Yüksek Lisans, İnşaat Mühendisliği Bölümü

Tez Yöneticisi: Prof. Dr. Haluk Sucuoğlu

Ortak Tez Yöneticisi: Prof. Dr. Barış Binici

Ocak 2013, 63 sayfa

Hasar almaya yatkın binalardaki sismik tehlikeyi azaltmak için, riskli olduğu belirlenen binalar

değerlendirilmeli ve güçlendirilmelidir. Zayıf binaların performans değerlendirmesi geçmişteki yıkıcı

depremler nedeniyle önemli bir mesele haline gelmiştir. Tasarım ve değerlendirme

yönetmeliklerindeki yeni koşulları doğrulamak için deney ve analiz yapmak gereklidir.

Bu çalışmada, Orta Doğu Teknik Üniversitesi Yapı ve Deprem Laboratuvarı’nda inşa edilmiş ve

dinamik benzeri deney yöntemi ile test edilmiş yönetmeliğe uygun olmayan iki betonarme çerçevenin

davranışı incelenmiştir. Söz konusu çerçeveler Deprem Bölgelerinde Yapılan Binalar Hakkında

Yönetmelik (DBYBHY 2007) ve ASCE/SEI 41-06’da belirtilen metodlar takip edilerek OpenSees

platformunda modellenmiştir. Bu çalışmanın odak notkası olan yetersiz bindirmeli eklerin bir

çerçevede bulunması haricinde, her iki yönetmeliğe uygun olmayan çerçeve de aslen aynıdır.

Zaman tanım alanında hesap yöntemi ile performans değerlendirmeleri DBYBHY 2007 ve ASCE/SEI

41-06’nın performans limitlerine göre yapılmıştır. Gözlemlenen hasarlar DBHBHY 2007’de belirtilen

prosedürle hesaplananan performans seviyelerile iyi bir şekilde örtüşmüştür. Bindirmeli ek

yetersizliği olan numune için ASCE/SEI 41-06 değerlendirmede fazla güvenli sonuç vermiştir.

DBHBHY 2007’nin bindirmeli ek boyu ile ilgili koşullarının fazla güvenli olduğu laboratuvarda

bulunmuş ve mevcut gerekli uzunluğun %25’ine kadar yetersizliğin tolere edilebildiği

gözlemlenmiştir.

Matematiksel modellere göre, yönetmeliğe uygun olmayan sistemlerde malzeme dayanım

özelliklerinin nominal değerlerin azaltılmışlarını kullanmak çok etkili değildir. Ayrıca, kolon-kiriş

birleşim bölgesi deformasyonları açık bir şekilde hesaba katılmadığı sürece lokal deformansyonlar

yakalanamamaktadır.

Anahtar Kelimeler: Dinamik Benzeri Test Yöntemleri, Numerik Simulasyonlar, Performans

Değerlendirmesi, Bindirmeli Ek Yetersizlikleri

vi

ACKNOWLEDGEMENTS

It would not have been possible to write this thesis without the help and support of the people in my

life. There are too many to mention everyone by name; if I thanked them all, the acknowledgements

would be longer than my thesis! Above all, I would like to thank my mother, Mei-Mei Cheng, who

has encouraged and supported me my whole life. I am forever indebted to my father, Oscar Po-Hsiu

Lin, for his decision to immigrate to Canada in pursuit of a better life for his family, May he rest in

peace. To my sisters Milly and Tina, my thanks for their understanding on the various decisions I

have made and will make in my life.

This thesis would not have been possible without the guidance and direction of my principal

supervisor, Dr. Haluk Sucuoğlu, and my co-supervisor, Dr. Barış Binici at the Middle East Technical

University. I thank the following professors at the University of British Columbia, in chronological

order, who encouraged me to pursue a career in academia: Dr. Reza Vaziri, Dr. Siegfried Stiemer, and

Dr. Kenneth Elwood.

To my friends in the simulations laboratory, I am grateful for the various forms of support you have

provided me. To Umair Ahmed Siddiqui, you will always be my “yar”.

I would like to acknowledge the financial support of the European Commission under the scope of its

Erasmus Mundus programme, and the Scientific and Technological Research Council of Turkey

(Tübitak), both of which provided the necessary funds that enabled me to pursue my Masters degree

abroad.

For any errors or inadequacies that may remain in this work, the responsibility is entirely my own.

vii

TABLE OF CONTENTS

ABSTRACT .......................................................................................................................................... iv

ÖZ .......................................................................................................................................................... v

ACKNOWLEDGEMENTS .................................................................................................................. vi

TABLE OF CONTENTS ..................................................................................................................... vii

LIST OF TABLES ................................................................................................................................ ix

LIST OF FIGURES ................................................................................................................................ x

CHAPTERS ........................................................................................................................................... 1

1. INTRODUCTION ................................................................................................................... 1

1.1 General ............................................................................................................................. 1

1.2 Analyses Methods ............................................................................................................ 2

1.3 Seismic Assessment Models............................................................................................. 2

1.4 Modelling Deficient Lap Splices ...................................................................................... 4

1.5 Objectives and Scope ....................................................................................................... 5

2. PSEUDO-DYNAMIC TESTING ............................................................................................ 7

2.1 General ............................................................................................................................. 7

2.2 Test Specimens ................................................................................................................. 8

2.3 Testing and Instrumentation ........................................................................................... 11

2.4 Test Results .................................................................................................................... 15

2.4.1 Specimen #1 ............................................................................................................... 15

2.4.2 Specimen #2 ............................................................................................................... 19

2.5 Comparison of Test Results............................................................................................ 23

3. NUMERICAL MODELS ...................................................................................................... 29

3.1 General ........................................................................................................................... 29

3.2 Specimen #1 ................................................................................................................... 30

3.3 Specimen #1-Comparison with Experimental Results ................................................... 30

3.4 Specimen #2 ................................................................................................................... 38

3.5 Specimen #2-Comparison with Experimental Results ................................................... 38

viii

3.6 Performance Evaluation of Test Frames ........................................................................ 45

3.6.1 Pushover and Time History Analysis Procedures ...................................................... 47

3.6.2 Specimen #1 Performance Evaluations ...................................................................... 47

3.6.3 Specimen #2 Performance Evaluations ...................................................................... 51

3.6.4 Discussion .................................................................................................................. 57

4. CONCLUSIONS ................................................................................................................... 59

4.1 General ........................................................................................................................... 59

REFERENCES ..................................................................................................................................... 61

ix

LIST OF TABLES

TABLES

Table 2. 1 Reinforcement details and moment capacities of columns .................................................. 11

Table 2. 2 Reinforcement details and moment capacities of beams ..................................................... 11

Table 2. 3 Column shear capacities, demands, and capacity/demand ratios ........................................ 11

Table 2. 4 Concrete strength and axial load ratios of columns ............................................................. 12

Table 2. 5 Ground motion properties ................................................................................................... 13

Table 2. 6 Maximum base shear, roof displacement and 1st storey drift comparisons ......................... 25

Table 3. 1 Peak roof displacement error (SP1) ..................................................................................... 34

Table 3. 2 Peak base shear error (SP1) ................................................................................................. 34

Table 3. 3 Peak inter-storey drift error (SP1) ....................................................................................... 34

Table 3. 4 Peak storey shear error (SP1) .............................................................................................. 34

Table 3. 5 Peak roof displacement error (SP2) ..................................................................................... 42

Table 3. 6 Peak base shear error (SP2) ................................................................................................. 42

Table 3. 7 Peak inter-storey drift error (SP2) ....................................................................................... 42

Table 3. 8 Peak storey shear error (SP2) .............................................................................................. 42

Table 3. 9 TEC damage state limits ..................................................................................................... 45

Table 3. 10 ASCE performance limits ................................................................................................. 46

Table 3. 11 Specimen #1 1st storey column performance levels .......................................................... 57

Table 3. 12 Specimen #2 1st storey column performance levels .......................................................... 57

x

LIST OF FIGURES

FIGURES

Figure 2. 1 Plan view of prototype building and test frame ................................................................... 8

Figure 2. 2 Elevation view of the test specimens ................................................................................... 9

Figure 2. 3 Specimen #1 and #2 beam, column and joint details ......................................................... 10

Figure 2. 4 Test specimen and pseudo-dynamic testing system scheme .............................................. 12

Figure 2. 5 Response and acceleration spectra ..................................................................................... 14

Figure 2. 6 Measurement devices and their configurations .................................................................. 15

Figure 2. 7 Roof displacement time history/observed damages (SP1) ................................................. 17

Figure 2. 8 Inter-storey drift ratio time histories (SP1) ........................................................................ 18

Figure 2. 9 Damages observed in the 3rd

storey columns (SP1) ........................................................... 18

Figure 2. 10 Storey shear forces vs. drift response (SP1) ..................................................................... 19

Figure 2. 11 Roof displacement time history/observed damages (SP2) ............................................... 21

Figure 2. 12 Damage observed at peak displacement (SP2) ................................................................ 21

Figure 2. 13 Inter-storey drift ratio time histories (SP2) ...................................................................... 22

Figure 2. 14 Reinforcement pullout at spliced regions (SP2) ............................................................... 22

Figure 2. 15 Storey shear force vs. drift response (SP2) ...................................................................... 23

Figure 2. 16 1st Storey drift time history comparisons ......................................................................... 24

Figure 2. 17 Base shear vs. roof displacement comparison .................................................................. 25

Figure 2. 18 1st mode period time history comparisons ....................................................................... 26

Figure 2. 19 Column 101 base and beam 111 left end rotation time history comparisons ................... 27

Figure 3. 1 OpenSees model with force-based elements ...................................................................... 30

Figure 3. 2 Roof displacement time history comparison (SP1) ............................................................ 31

Figure 3. 3 Inter-storey drift ratio time history comparisons (SP1) ..................................................... 32

Figure 3. 4 Storey shear force time history comparisons (SP1) ........................................................... 33

Figure 3. 5 Comparisons of bottom end curvatures of 1st storey columns (SP1) ................................. 35

Figure 3. 6 Comparisons of top end curvatures of 1st storey columns (SP1)........................................ 37

Figure 3. 7 Roof displacement time history comparison (SP2) ............................................................ 39

Figure 3. 8 Inter-storey drift ratio time history comparisons (SP2) ..................................................... 40

Figure 3. 9 Storey shear force time history comparisons (SP2) ........................................................... 41

Figure 3. 10 Comparisons of bottom end curvatures of 1st storey columns (SP2) ............................... 43

Figure 3. 11 Comparisons of top end curvatures of 1st storey columns (SP2)...................................... 44

Figure 3. 12 Damage/performance limits and performance levels ....................................................... 46

Figure 3. 13 Specimen #1 performance evaluation w.r.t. TEC damage state levels (experimental peak

demands) .............................................................................................................................................. 48

xi

Figure 3. 14 Specimen #1 performance evaluation w.r.t. ASCE performance levels (experimental peak

demands) .............................................................................................................................................. 48

Figure 3. 15 Specimen #1 performance evaluation w.r.t. TEC damage state levels (time history peak

demands) .............................................................................................................................................. 49

Figure 3. 16 Specimen #1 performance evaluation w.r.t. ASCE performance levels (time history peak

demands) .............................................................................................................................................. 50

Figure 3. 17 Specimen #1 1st storey column damages during D2 ........................................................ 50

Figure 3. 18 Specimen #1 capacity curve and demands ....................................................................... 51

Figure 3. 19 Specimen #2 performance evaluation w.r.t. TEC damage state levels (experimental peak

demands) .............................................................................................................................................. 52

Figure 3. 20 Specimen #2 performance evaluation w.r.t. ASCE performance levels (experimental peak

demands) .............................................................................................................................................. 52

Figure 3. 21 Specimen #2 1st storey column damages during D2 ........................................................ 53

Figure 3. 22 Specimen #2 performance evaluation w.r.t. TEC damage state levels (time history peak

demands, TEC splices) ......................................................................................................................... 54

Figure 3. 23 Specimen #2 performance evaluation w.r.t. ASCE performance levels (time history peak

demands, ASCE splices) ...................................................................................................................... 54

Figure 3. 24 Specimen #2 capacity curve and demands (TEC splices) ................................................ 55

Figure 3. 25 Specimen #2 capacity curve and demands (ASCE splices) ............................................. 56

Figure 3. 26 Base shear vs. roof displacement responses and capacity curves .................................... 56

1

CHAPTERS

1. INTRODUCTION

1.1 General

Many reinforced concrete buildings around the world are insufficiently designed and/or constructed,

according to modern seismic codes, regulations, and best practices. In order to reduce seismic risk in

vulnerable buildings, buildings identified to be at risk should be assessed and strengthened. In recent

history, there has been an absence of technical standards for risk reduction processes.

Performance evaluation of deficient buildings has become a major concern due to recent devastating

earthquakes in Turkey which caused significant economic and human loss. Preliminary seismic

performance assessments funded by the government of Turkey had revealed that a significant number

of buildings have numerous deficiencies. The most observed deficiencies are as follows: plan

irregularities, presence of heavy overhangs, poor detailing in structural members and joint regions,

low material strengths, inadequate member sizes and finally, the use of plain reinforcements, which is

of particular interest to this study. Buildings constructed before the 1980s had splices which were

designed for compression only, leading to insufficient development lengths in tension.

Different deficiencies have various local and global effects on the seismic performance of buildings

and should thus be studied separately. Proper rehabilitation of existing buildings before a major

earthquake hits is of utmost importance, as many populated cities in Turkey are located in high

seismic zones.

To the best of the author’s knowledge, the effect of lap splice deficiencies have mostly been examined

in the literature via individual column tests, such as the tests conducted by Aboutaha et al. (1996),

Lynn et al. (1996), Melek and Wallace (2004), and Eshghi and Zanjanizadeh (2007). There are a

limited number of frame tests investigating the behaviour of columns with insufficient splice lengths,

such as the tests conducted by Canbay (2003) and Akin (2011). However, frame test with such

deficiencies tested under realistic earthquake demands are scarce. Thus, the opportunity to examine

lap splice deficiencies and their local and global effects on reinforced concrete frames subjected to

earthquake ground motions would greatly benefit the engineering community.

Released in 1997, FEMA 273 (Guidelines for the Seismic Rehabilitation of Buildings) was one of the

leading global comprehensive documents which proposed various technical requirements for the

seismic rehabilitation of existing buildings. Soon after, in 2000, FEMA 356 (Prestandard and

Commentary for the Seismic Rehabilitation of Buildings) replaced FEMA 273 and became the new

benchmark document. Methods outlined in FEMA 356 served as a basis for future developments and

research topics of many codes and regulations around the globe. As this document was revised and

improved over time, it was replaced by ASCE/SEI 41-06 (Seismic Rehabilitation of Existing

Buildings) in 2006. In 2007, a document titled ASCE/SEI 41 Supplement-1, based on research on the

proposed effective stiffness models, modeling parameters, and acceptance criteria, was released. This

supplement to the original ASCE/SEI 41 contained provisions related to the rehabilitation of existing

reinforced concrete buildings. ASCE/SEI 41-13 is scheduled to be released in 2013, but there are

virtually no changes for the reinforced concrete provisions outlined in the first supplement.

The current seismic building code in Turkey, the Turkish Earthquake Code 2007 (TEC 2007), was

released in 2007 and provides evaluation methods and performance limits for use in building design.

The procedures outlined in TEC 2007 are similar to those of ASCE/SEI 41-06. However, for the first

time in design code history, the Ministry of Construction and Resettlement in Turkey added a section

2

regarding the assessment and strengthening of existing buildings to TEC 2007 in 2007, employing a

performance-based vision. The procedures outlined in TEC 2007 need detailed verification studies, as

they slightly differ from the point defining the member acceptance criteria. Leading earthquake

engineering countries such as the USA and Japan do not have legal documents regarding this matter

and thus renders comparative analyses impossible. As mentioned before, Turkey is in an urgent

situation in terms of the amount of seismic rehabilitation needed in the country. Thus, research on the

reliability of these proposed methods is essential for future revisions and improvements on the current

code.

1.2 Analyses Methods

There are two main groups of analysis procedures which are deemed acceptable in the engineering

community for the estimation of seismic demands of structures: Response spectrum and dynamic

analyses. Static and dynamic analyses can both be linear or nonlinear, each varying in computational

effort and accuracy.

Static analysis methods estimate the dynamic ground motion input response through statistical modal

combination rules, which inherently introduce errors into the analysis since directional combination of

the modal responses is ignored. These errors are more prominent when estimating member forces as

statistical combination rules generally predict a higher capacity. Using nonlinear static (pushover)

analysis is often seen as an acceptable trade-off between accuracy and computational effort for low to

mid-rise buildings, as it normally yields sufficiently accurate results for engineers. This procedure

applies a lateral static force profile to the structure until the desired target displacement is reached.

Within nonlinear static analysis, there are various ways to apply this force vector. The most

conventional method is to use the first mode’s force vector, obtained from the first mode shape of the

structure through classical structural dynamics theory. This is an acceptable procedure for structures

which are primarily first mode dominant, which is the case of the test specimens discussed in this

thesis study. The inability of conventional nonlinear static analysis for capturing higher mode effects

is recognized, and for structures which are not first-mode dominant, adaptive pushover analysis

procedures were proposed by Chopra and Goel (2002). As discussed in a later section, the test

specimens studied in this thesis are first-mode dominant. Therefore, higher mode effects are not

expected.

Nonlinear dynamic (time history or response history) analysis procedure is accepted as the most

accurate amongst all four types of analysis methods. However, this type of analysis requires the

highest computational effort in terms of run time, computing power, and post-processing as it is the

most complex method of all. Convergence and stability problems are the most common issues which

arise, and are especially present in computer software. The sources of these errors are difficult to

detect and solve.

This study will focus on nonlinear static and nonlinear dynamic analyses, with both methods being

implemented on the OpenSees platform for the test specimens.

OpenSees is an acronym for Open System for Earthquake Engineering Simulation and is an object-

oriented, open-source software created at the Pacific Earthquake Engineering Center. The program is

used for finite element modelling in the simulation of the response of structural and geotechnical

systems subjected to earthquakes. OpenSees is able to model and analyze the nonlinear static and

dynamic response of systems using various material models, elements, and solution algorithms.

1.3 Seismic Assessment Models

During a ground excitation, lateral loads imposed by earthquakes on a conventional reinforced

concrete frame are carried by the gravity load-bearing columns of the structure. Thus, these columns

need to be adequately designed in order to have the sufficient strength and ductility required from the

force and displacement demands of an earthquake. When designing a reinforced concrete structure, it

is imperative that an estimation of column ductility be as accurate as possible, as this is one of the

main governing factors of its seismic performance and failure mechanisms.

3

In performance-based assessments, individual structural members are classified according to their

expected failure modes based on their nonlinear deformation capacities. These classifications are then

used to determine modelling parameters and deformation limits for a pre-defined performance level.

In the original ASCE/SEI 41-06, provisions for modelling parameters and numerical acceptance

criteria of reinforced concrete elements were not classified based on flexure failure, shear failure,

shear/flexure failure, or inadequate lap splicing. It is stated in EERI/PEER (2006) that the original

proposed acceptance criteria from ASCE/SEI 41-06 yield conservative results. Furthermore, a study

conducted by Sezen and Moehle (2006) showed the existence of limited plastic deformation

capacities of columns due to flexural yielding prior to shear failure, commonly known as the flexure-

shear failure. Thus, a revision of ASCE/SEI 41-06’s deformation limits was required in order to

improve future estimations.

Classifications of columns for determining modelling parameters were revised and published in

ASCE/SEI 41 Supplement-1, which included the flexure-shear failure mode. In this supplement, three

conditions are defined and classification of columns is obtained through its shear capacity/demand

ratio and the transverse reinforcements of critical sections. Once classified, modelling parameters and

acceptance criteria can be obtained for each type of failure mode: flexure, flexure-shear, and shear.

However, Acun and Sucuoglu (2010) suggested that the new deformation-based performance limits

proposed for nonconforming columns were still conservative in setting the rotation limits of life

safety and collapse prevention, which may yield misleading results in the seismic risk assessment of

existing concrete structures. They noted that the performance limits also appeared to be very

conservative in predicting the experimental performance of column plastic hinges designed to fail in

pure flexure under moderate axial load levels.

In Chapter 7 (“Seismic Assessment and Retrofit Design of Existing Buildings”) of TEC 2007,

structural members are classified into either ductile or brittle failure, which correspond to flexure and

shear failure as defined in FEMA 356, respectively. TEC 2007 has yet to include the flexure-shear

mode in its classification procedures, which is essential in order to accurately estimate member

modelling parameters and acceptance criteria.

It is essential in both linear and nonlinear modelling that joint strength and flexibility capacities are

captured as accurately as possible. Earthquake-induced deformations in moment resisting frames

cause moment reversals at beam-column joints which may induce high shear demands in these

regions. Unless rigorously modelled, frame stiffness reduction and/or premature strength loss may not

be captured correctly.

Before the onset of plasticity, the elastic portion of a beam-column joint behaviour can be modelled

with rigid end offsets of various lengths to model the joint flexibility.

In FEMA 356, the simple approach of setting rigid end offsets equal to the joint dimensions is

recommended. ASCE/SEI 41-06 refined this approach by defining rigid end offset lengths as a

function of the flexural strength of connected beam-columns. In the case of a strong column-weak

beam system, rigid offsets are only required for columns, whereas in a strong beam-weak column

system, rigid offsets are only recommended for beams. For intermediate cases, half the length of the

joint dimension is modelled as the rigid offset length for columns and beams at the joint. TEC 2007

states that full rigid offsets are defined for both the columns and beams.

In a recent study by Birely et al. (2012), recommended procedures from FEMA 356 and ASCE/SEI

41-06 for rigid offsets were evaluated in light of 45 experiments. The main findings were: i) defining

rigid offsets as per FEMA 356 resulted in overly stiff models and using ASCE/SEI 41-06 resulted in

more realistic values; ii) FEMA 356 predicts an overly stiff model which inaccurately predicts the

initial yield displacements of experiments, while ASCE/SEI 41-06’s predictions are generally good,

except for in the case of joints which do not satisfy the requirements of ACI 318-08. Thus, it was

recommended that an alternative definition of rigid offsets be set for joint compliance/non-compliance

with ACI 318-08, in order to improve the estimation of initial yield displacements.

4

The behaviour of beam-column joints has been an extensive researched topic in the past, resulting in

the general conclusion that joints may experience high shear deformations prior to the yielding of

longitudinal reinforcement. Once beam-column joints enter the plastic region, proper modelling of

their nonlinear behaviour becomes an important factor in accurate simulations.

1.4 Modelling Deficient Lap Splices

The strength from steel reinforcement in concrete is primarily achieved through two mechanisms:

mechanical interlock between the concrete and reinforcing steel (only in deformed rebar), and

frictional strength due to the cement chemical bond. Since the specimens of interest in this

dissertation only contain plain reinforcing steel, strength is only developed due to friction achieved by

chemical bonds.

In order to ensure proper strength development in reinforcement, proper control of sufficient bar

spacing/cover, use of transverse reinforcement, and minimizing bar sizes are needed. In most design

codes, the development length is a function of:

The rebar diameter;

The concrete strength/density;

The concrete cover;

The steel strength;

The location of the rebar in beams (top or bottom)

The quality of the bond due to vibration; and

The presence of epoxy coating

It is of interest to understand the effects of inadequate lap splices because structures with such

deficiencies exist all around the world, and a reliable method in assessing and strengthening buildings

would greatly benefit the engineering community. Inadequate lap splices in a structure often result in

premature failure which in turn leads to injuries and/or casualties in the event of an earthquake.

A structure’s strength and deformation response are highly affected by the lap splice length.

Insufficient ductility of a structure arises from insufficient transverse reinforcement (due to

insufficient confinement) and insufficient lap splices in the plastic hinge zone.

When design provisions of a building code are not met, the deficiencies greatly diminish its capacity.

In seismic assessment, guidelines usually do not require each of these deficiencies be modelled on a

local scale, but recommend implicit methods to account for their effects.

The following list summarizes various research teams which have proposed formulae for determining

the bond strength between lap-spliced reinforcement and concrete:

Orangun et al. (1977) – considered concrete cover, bar diameter, lap-splice length, material properties, and amount of transverse reinforcement;

Eligehausen et al. (1983) – considered unconfined and well-confined concrete and proposed a model which includes ascending, yielding, softening, and a final constant stress zone;

Soroushian et al. (1991) – considered effects of confinement and concrete strength on local slip conditions of deformed bars;

Xu (1992) – considered bond strength through experimental statistical regression and stress-state analysis;

Harajli (1994) – considered reinforcement in plain and fibre-reinforced concrete

Priestley et al. (1996) – considered fracture mechanics;

Xiao et al. (1997) – considered modifications to pre-existing ACI definitions;

Ghobarah et al. (2003) – considered the effect of bar slip on the flexural strength of columns;

Sezen et al. (2003) – considered the effect of bar slip on deformations with a focus on rigid body rotations due to bar elongation and slip in the joints (strain penetration effect);

Zhao et al. (2006) – proposed a zero length element capable of modelling the strain penetration effect

5

As suggested in TEC 2007 and ASCE/SEI 41-06, joint/lap splice deficiencies in mathematical models

are indirectly accounted for through a reduction factor of steel yield strength. In the case of TEC

2007, this factor is a linear reduction in proportion to the splice length to development length ratio,

whereas the factor in ASCE/SEI-41-06 is an exponential factor of the same ratio. The presence of

insufficient lap splice lengths that decrease a structure’s capacity in analyses is based on various

experimental results.

1.5 Objectives and Scope

In order to justify new provisions in design and assessment codes, experiments and analyses are

inherently necessary. This ensures that modelling parameters are adequate enough for accurate

seismic assessment and rehabilitation of existing structures. The Scientific and Technological

Research Council of Turkey (Tübitak) funded a research project at Middle East Technical University

(METU)’s Structural and Earthquake Laboratory for the verification and validation of the existing

assessment and performance-based design methodologies in TEC 2007 through analyzing and testing

various concrete frames.

The project is titled: “Developing Performance-Based Evaluation Procedures and Strengthening

Methods for the Turkish Seismic Code through Experimental and Analytical Research” and is

officially documented as “TÜBİTAK 1007, Project #108G034”.

The project has a duration of 36 months and commenced on February 15, 2010. This thesis

investigates the behaviour of test specimens, Specimen #5 (hereinafter referred to as Specimen #1)

and Specimen #9 (hereinafter referred to as Specimen #2), which the author will model by following

the methods of analyses as outlined in TEC 2007 and ASCE/SEI-41-06. Lap splice modelling

recommendations as per the two documents will be compared to their respective experimental results.

Each physical test frame constructed in the laboratory is essentially a ½ scale 3-storey and 3-bay

frame of the project’s prototype reinforced concrete frame, but differs slightly with respect to code

conformations and deficiencies. This ½ scaling is based on principles of equal stresses between the

full scale prototype frame and the scaled test specimen, leading to half the displacements of the

prototype frame but equal inter-storey drifts. The frames were subjected to simulated seismic

excitation through the pseudo-dynamic testing procedure.

The following objectives are set forth in this thesis:

Evaluation of pseudo-dynamic test results of two deficient reinforced-concrete frame specimens, one with lap splice deficiencies and one without;

Calibration of OpenSees models of test specimens through numerical simulations and comparison of accuracies obtained from different modelling techniques;

Investigation of local deformation components, and their interactions and contributions to the global response of the specimens using calibrated models;

Present and comment on the effects of the presence of lap splices on local and global behaviours in the physical frame and computer models;

Evaluation of strain-based nonlinear performance assessment procedures as outlined in TEC 2007 and the rotation-based nonlinear performance assessment procedures outlined in

ASCE/SEI 41-06 in light of experimental observations; and

Suggest future directions for an improved performance-based design and assessment code

Chapter 2 briefly presents an overview of the experimental setup and the specimens’ results.

Numerical simulations of Specimen #1 and Specimen #2 are presented in Chapter 3 in comparison

with experimental results and observations. Since Specimen #1 is the reference specimen without

splices, the calibration of the computer model is also presented in Chapter 3. Special attention is given

to the effects of lap splices in the deficient specimen. The modelling results of the various building

code recommendations on accounting for deficient lap splices are compared with the experimental

results. While the global behaviour of the results is examined, selected beams and columns are

examined in detail on a local scale using the calibrated computer models of the test specimens. This

6

chapter also presents the results of the performance evaluations conducted on the specimens, along

with comparisons to the experimental damages.

Lastly, in Chapter 4, a summary with the main conclusions of this thesis are presented with future

research recommendations.

7

2. PSEUDO-DYNAMIC TESTING

2.1 General

Two specimens were built and tested at METU’s Structural Mechanics Laboratory as a part of

108G034 Tübitak’s project on performance-based design and assessment of reinforced-concrete

buildings. Significant contributions in the laboratory were provided by Mehmet Engin Ayatar,

Pourang Ezzatfar, and Mahdi Ghaffarinia. This chapter discusses the testing procedures and

summarizes the experimental results for these two specimens.

Both specimens were deficient bare frames, as they were not compliant according to the provisions of

TEC 2007. Deficiencies included the use of low strength concrete, plain reinforcing steel, minimum

flexure reinforcement, insufficient confinement, and insufficient shear strength. Specimen #2

(referred to as SP2 in tables and figures) was essentially the same as Specimen #1 (referred to as SP1

in tables and figures), but with the presence of insufficient lap splices for column longitudinal

reinforcement at plastic hinge regions (75% of the length required by TEC = 75% x 40db). Specimen

#1 had continuous bars throughout the beams and columns and Specimen #2 only had continuous bars

throughout the beams.

The prototype structure’s plan view is presented in Figure 2.1. The test frame of interest is the frame

along gridline 3. As mentioned before, each test frame constructed in the laboratory was a ½ scale 3-

storey and 3-bay frame of the project’s prototype reinforced concrete frame. All frames were designed

for a typical Turkish building located in the first seismic zone on Z3 (highly weathered soft

metamorphic rock, medium dense sand and gravel, stiff clay and silty clay) soil type, with

aforementioned deficiencies.

Continuous pseudo-dynamic testing was conducted for both specimens using synthetic ground

motions compatible with the site-specific earthquake spectra developed for the city of Düzce, as a

result of the earthquake which occurred in 1999.

Analytical verification of scaling of the test specimen and ground motions was verified by preliminary

pushover and time-history analyses in the 1st project progress report (2010). When compressed in the

time domain with a factor of according to the similitude law, the original ground motion produced the desired earthquake demands on the ½-scaled prototype specimens.

8

Figure 2. 1 Plan view of prototype building and test frame

2.2 Test Specimens

The member sizes and longitudinal reinforcement details of the prototype building was designed

according to TEC 2007. The column dimensions were 400 mm x 300 mm with approximately a

1.33% longitudinal reinforcement ratio. The beam dimensions were 300 mm x 350 mm, which were

uniform in all spans. The interior bay frame (Figure 2.1, gridline 3) was selected as the test specimen.

The test specimens’ dimensions were taken as ½ of the prototype frame member sizes, as shown in

Figure 2.2, along with the notation for the beams and columns.

9

Figure 2. 2 Elevation view of the test specimens

The average uniaxial compressive strength of concrete used for Specimen #1 was 11.9 MPa. The

column longitudinal reinforcement steel had a yield strength of 320 MPa, whereas the beam

longitudinal reinforcement steel had 355 MPa, and the transverse reinforcement had 240 MPa, as

determined from material tests. Detailed section drawings of Specimen #1, shown in Figure 2.3, were

the same for the elements in each storey and each axis of the test frame.

The average uniaxial compressive strength of concrete used for Specimen #2 was 14.0 MPa. The

reinforcement material strengths were the same as specimen #1, as the steel was obtained from the

same batch. Specimen #2 had the same member dimensions as Specimen #1 and the only difference

was that there was twice the amount of longitudinal reinforcing steel in the spliced regions.

In TEC 2007, the shear force demand on a column (Ve = (Mt+Mb)/ln) is determined by using the top

and bottom plastic moment values (Mt and Mb) of the columns, for a weak column-strong beam

system, where ln is the clear height. A weak column-strong beam system is defined in TEC 2007

when the plastic moments of the columns are less than 1.2 times the plastic moments of the beams

connecting into a joint, which is the case for both specimens (see Mp values in Table 2.1 and Table

2.2). Most joints in the specimens satisfy this condition for a weak column-strong beam, with the

exception being the exterior joints at the 1st and 2

nd storeys.

The shear force resistance Vr is defined as:

(2.1)

where fctd is the concrete tensile strength, bw is the column width, d is the column depth, Asw is the area

of the shear reinforcing steel, s is the spacing of the transverse reinforcing steel, and fywd is the

strength of the transverse reinforcing steel.

10

The condition of insufficient shear capacity (Vr < Ve) corresponds to a shear-flexure failure mode

(condition (ii) as defined by ASCE/SEI 41-06). In TEC 2007, there is no intermediate failure mode

between shear and flexure failure defined and as such, this condition is classified as a shear failure

mode.

Both specimens had deficient material strengths, reinforcement amounts, reinforcement details, and

joint details. These deficiencies reflect the typical characteristics of the most common existing

deficiencies in Turkey.

The properties of the test frames can be summarized as follows:

The column longitudinal reinforcement was approximately 1.33%;

Plain reinforcement bars with 8 mm and 10 mm diameters were used for the columns and beams, respectively;

The yield strength of the 8 mm and 10 mm diameter bars were 320 MPa and 355 MPa, respectively;

The ultimate strengths of these bars were 460 MPa and 555 MPa, respectively;

6 mm plain reinforcement bars were used as transverse reinforcement;

The mean values of uniaxial concrete compressive strength (Specimen #1 – 11.9 MPa, Specimen #2 – 14.0 MPa) were determined from standard cylinder tests;

The flexural and shear capacity of the beams were designed to be sufficient for gravity loads;

The conventional strong-column weak-beam requirement was violated in these specimens;

The transverse reinforcement spacing of the columns was kept constant throughout the column height, which resulted in unconfined zones at element potential plastic hinge regions;

and

Lateral reinforcements were absent at joints to reflect joint shear deficiencies

Detailed section and joint drawings of Specimen #1 and #2 are presented in Figure 2.3. The detailing

was the same for the elements in each storey and each axis of the test frame.

Beam (Support Regions) Beam (Span Regions)

Column Joint

Figure 2. 3 Specimen #1 and #2 beam, column and joint details

11

Longitudinal and shear reinforcement details, and moment capacities of columns and beams,

calculated using the nominal strength values of both specimens, are presented in Table 2.1 and Table

2.2, respectively. For Specimen #2, moment capacities of column bases were calculated by applying

the linear reduction suggested in TEC 2007 to the moment capacities of Specimen #1. Using

ASCE/SEI 41-06’s exponential reduction would have resulted in a higher resisting moment capacity

and higher plastic moment capacity and thus, more conservative results. The top regions of columns

in Specimen #2 had the same capacities as Specimen #1.

Table 2.3 presents the shear capacities and capacity/demand ratios of the columns, calculated using

the nominal strength values (without safety factors) for the two frames according to TS 500 (2000).

The columns in both specimens are not shear critical, as the ratios are greater than 1.0.

It should be noted again that all the reinforcement bars used in columns and beams of the both

specimens were plain bars.

Table 2. 1 Reinforcement details and moment capacities of columns

Specimen

Reinforcement Details Moment Capacity [kNm]

Long.

(Mid)

Long.

(End)

Lat.

(Mid)

Lat.

(End) Mr Mp

#1 (Outer) 8Ø8 8Ø8 2xØ4/100 2xØ4/100

11.4 13.6

#1 (Inner) 12.8 14.5

#2 (Outer) 8Ø8 16Ø8 2xØ4/100 2xØ4/100

8.6 10.2

#2 (Inner) 9.6 10.9

Table 2. 2 Reinforcement details and moment capacities of beams

SP

Reinforcement Details Moment Capacity [kNm]

Long.

(Support, i)

Long.

(Span, ii)

Trans.

(Support, i)

Trans.

(Span, ii) Mr(i) Mr(ii) Mp(i) Mp(ii)

#1 4Ø10+3Ø10 2Ø10+3Ø10 Ø4/50 Ø4/80 17.9 11.9 20.7 16.3

#2 4Ø10+3Ø10 2Ø10+3Ø10 Ø4/50 Ø4/80 18.1 12.1 20.9 16.9

Table 2. 3 Column shear capacities, demands, and capacity/demand ratios

Specimen Vr [kN] Ve [kN] Vr/Ve

#1 (Outer) 26.6 19.8 1.34

#1 (Inner) 26.6 21.1 1.26

#2 (Outer) 29.0 17.3 1.68

#2 (Inner) 29.0 18.5 1.57

2.3 Testing and Instrumentation

The dead and live loads remained constant throughout each pseudo-dynamic test. Gravity dead loads

were applied through the use of steel blocks, as shown in Figure 2.2. The blocks were arranged such

that the ratio of axial load to the axial load carrying capacity of the columns of the specimens is

similar to the prototype frame. The axial load ratios of columns under gravity loads are presented in

Table 2.4, where N is axial load experienced at the columns from the self-weight of the frame and the

steel blocks which account for the transverse beams and slabs, and No = f’cAc is the axial load

carrying capacity of the columns.

12

Table 2. 4 Concrete strength and axial load ratios of columns

SP Mean f’c [MPa] 1

st Storey N/No Ratio

Inner Columns Outer Columns

#1 11.9 0.228 0.133

#2 14.0 0.195 0.114

Pseudo-dynamic testing is a hybrid earthquake simulation technique which combines numerical

modelling of the structural properties with a physical test run in parallel with computations

(Takanashi et al. (1975), Mahin and Shing (1985), Nakashima (1985)). This testing method was

developed as an alternative to shake table testing. Through pseudo-dynamic testing, it is possible to

accurately simulate large-scale structural behaviour under seismic loads in a more practical way. Due

to the “pseudo-time” nature of the method, the general behaviour of the structure under the earthquake

loads can be closely monitored during the experiment.

In each pseudo time-step, restoring forces are measured by the load cells and the information

collected is used with the pre-defined input ground motion, mass, and damping properties to

determine the step-by-step numerical integration through the equation of motion. The displacements

for the successive steps are calculated and applied to the lateral degrees of freedom of the test

structure through servo-controlled hydraulic actuators. This is shown graphically in Figure 2.4 for the

case of the test specimens, which have three degrees of freedom.

Figure 2. 4 Test specimen and pseudo-dynamic testing system scheme

13

Figure 2.4 (Continued)

Ground motions used for the pseudo-dynamic tests were synthetic-time acceleration series of the 1999

Düzce earthquake, which were generated in a previous work package of the Tübitak research project.

They were compatible with the site-specific earthquake design spectra for different probabilities of

exceedance on different soil types, as shown in Table 2.5. Three of the generated acceleration series

from the previous work package (named D1, D2, and D3) were imposed on the test specimens

subsequently. Acceleration time series with the order of application and corresponding spectra of the

ground motions are shown in Figure 2.5.

Table 2. 5 Ground motion properties

Earthquake

GM

Probability of Exceedance

(50 Years) Soil Class/Type PGA [g]

D1 50% Z1/Rock 0.254

D2 10% Z1/Rock 0.545

D3 10% Z3/Soft Soil 0.604

14

a) Design Response Spectra

b) Acceleration Time History

Figure 2. 5 Response and acceleration spectra

Forces applied on the specimen were measured by the load cells built in the actuators of the pseudo-

dynamic testing system at each storey of the test frames. Linear Variable Differential Transformers

(LVDTs) were used to measure the storey displacements and the displacements at the column and

15

beam ends of the 1st and 2

nd storeys. Transducer boxes at the 1

st storey outer columns were used to

measure the axial loads, shear forces, and moments. The configuration is shown in Figure 2.6.

Figure 2. 6 Measurement devices and their configurations

2.4 Test Results

Test results of both specimens are presented in this section. Storey displacements, inter-storey drift

ratios, and storey shear forces are presented, along with selected pictures showing certain damages

observed. Local demand parameters such as member end curvatures are discussed in the next chapter,

along with the numerical simulation results.

2.4.1 Specimen #1

The roof displacement time history response from the physical test is presented in Figure 2.7 along

with the damages observed at selected peak deformations. The inter-storey drift ratio time history

responses are presented in Figure 2.8. No damage was observed under D1, and the inter-storey drift

ratio was under 0.3% for each storey and the maximum roof displacement was 9.4 mm. The specimen

was in a minimum damage state after D1.

Under D2, the maximum inter-storey drift ratio experienced was 1.3% and the maximum roof

displacement was 49 mm. Major damages observed during D2 were flexural cracks in both the

interior and exterior columns of the 1st storey, and the onset of visible cracks in the 1

st storey joint

regions (which initiated prior to cracks in the connecting beam and column ends). Both of these

16

damage formations were directly related to the lack of confinement in column ends and joint regions.

This implies that some inelastic deformations occurred in the 1st storey and parts of the specimen were

at most in a moderate damage state after D2.

Under D3, the macro-cracks at the bottom ends of the 1st storey columns continued to spread and

widen. Damages in the columns were followed by the spread of inclined crack in the joint regions and

flexural crack formations at the beam ends. The 1st storey drift ratio reached a maximum value of

4.1% and the maximum roof displacement reached a maximum value of 206 mm. The spread of

damage in the upper stories was in the form of shear cracks in the joints and flexural cracks in the

upper ends of the 2nd

and 3rd

storey columns. Inter-storey drift ratios of the higher storeys were higher

than 5%, greater than the 1st storey. The large deformations during the ground motions resulted in

high residual displacements towards the end of the pseudo-dynamic test. Large cracks at the top ends

of the 3rd

storey columns indicated that longitudinal reinforcement slip occurred. Figure 2.9 shows

damages observed at the top of the 3rd

storey columns, due to the lack of anchorage at that location.

The structure was in a severe damage state after D3.

Shear force vs. inter-storey drift ratio for each storey and base shear vs. roof displacement plots are

presented in Figure 2.10. The base shear vs. roof displacement plot shows severe strength degradation

and a softening response, implying that the specimen lost its lateral load carrying capacity.

17

Figure 2. 7 Roof displacement time history/observed damages (SP1)

18

Figure 2. 8 Inter-storey drift ratio time histories (SP1)

Figure 2. 9 Damages observed in the 3

rd storey columns (SP1)

19

Figure 2. 10 Storey shear forces vs. drift response (SP1)

2.4.2 Specimen #2

The roof displacement time history response from the physical test is presented in Figure 2.11, along

with the damages observed at selected peak deformations (Figure 2.12). The inter-storey drift ratio

time history response is presented in Figure 2.13. No damage was observed under D1, and the inter-

storey drift ratio was under 0.3% for each storey whereas the maximum roof displacement was

9.3mm. The specimen was in a minimum damage state after D1. Minor cracks were observed at the

1st storey columns at the peak of D1.

Under D2, the maximum inter-storey drift ratio experienced was 1.2% and the maximum roof

displacement was 55.1mm, similar to the values of Specimen #1. Major damage observed during D2

was flexural cracks in both the interior and exterior columns of the 1st storey, and the onset of visible

cracks in the 1st storey joint regions (which initiated prior to cracks in the connecting beam and

column ends). Both of these damage formations were directly related to the lack of confinement at

20

column ends and joint regions. This implies that some inelastic deformations occurred in the 1st storey

and the specimen was at most in a moderate damage state after D2, once again much like Specimen

#1. However, there was very little residual displacement observed after D2, contrary to that observed

in Specimen #1.

Under D3, the macro-cracks at the bottom ends of the base columns continued to spread and widen.

Damages in the columns were followed by the spread of inclined cracks in the joint regions and

flexural crack formations at the beam ends. The 1st storey drift ratio reached a maximum value of

4.3% and the maximum roof displacement reached a maximum value of 153 mm. Compared to

Specimen #1, the 1st storey drift ratio was similar, but the maximum roof displacement is significantly

reduced. The spread of damage in the upper stories was in the form of shear cracks in the joints and

flexural cracks in the upper ends of the 2nd

and 3rd

storey columns. Maximum inter-storey drift ratios

of the 2nd

and 3rd

storeys were 3.2% and 3.5%, respectively. The large deformations during the ground

motions did not result in high residual displacements, as was observed in Specimen #1. This can be

attributed to the presence of lap splices, which provided additional resisting forces in the spliced

regions. Large cracks at the ends of the columns indicated that the longitudinal reinforcement pullout

phenomenon due to the unconfined joints was also experienced, as shown in Figure 2.14. Contrary to

Specimen #1, there was no yielding at the top of the 3rd

storey columns. The structure was in a severe

damage state after D3.

Shear force vs. inter-storey drift ratio for each storey and base shear vs. roof displacement plots are

presented in Figure 2.15. The base shear vs. roof displacement plot does not show as severe strength

degradation and softening response as Specimen #1, implying that the specimen had a comparatively

larger lateral load carrying capacity after the ground motions.

21

Figure 2. 11 Roof displacement time history/observed damages (SP2)

Figure 2. 12 Damage observed at peak displacement (SP2)

22

Figure 2. 13 Inter-storey drift ratio time histories (SP2)

Figure 2. 14 Reinforcement pullout at spliced regions (SP2)

23

Figure 2. 15 Storey shear force vs. drift response (SP2)

2.5 Comparison of Test Results

Comparisons of the two specimens are presented in terms of the 1st storey drift ratio, base shear vs.

roof displacement response, selected beam/column rotations, and vibration periods of the 1st mode.

It should be reminded that ideally, the only difference between the two deficient specimens is the

presence of insufficient lap splices. However, other inherent factors to consider such as construction

methods, material strengths, and power outages during the pseudo-dynamic tests affected the results

of the experiments. Thus, these comparisons are presented in this section without detailed discussion

as this may lead to misleading interpretations.

The 1st storey drift ratio time histories for both specimens are presented in Figure 2.16. Base shear vs.

roof displacement responses are shown in Figure 2.17 and maximum recorded values of these

responses are provided in Table 2.6. Figure 2.18 shows the 1st period vibration mode variation time

24

history plots. Figure 2.19 shows the rotation time histories for column 101’s bottom end and beam

111’s left end.

The fundamental periods were determined by the procedures defined by Molina et al. (1999), where

the experimental displacements u(n), velocities v(n), and restoring forces’ r(n) relation is:

)(·1)()( nro

C

K

nvnu T

T

T

T

TT

(2.2)

where K and C are the secant stiffness and viscous equivalent damping matrices, respectively. o is a

constant force offset term. The equation contains “2·ndof2+ndof” unknowns and the number of

available equations is “N·ndof”, for N time intervals. By satisfying the condition that N>2·ndof+1 and

estimating K and C by a least mean squares algorithm, the complex eigen-frequencies and mode

shapes can be determined by solving the generalized eigenvalue equation:

00

0

0

w

M

Kw

M

MCs (2.3)

where M is the theoretical mass matrix, w contains the eigenvectors, and s is the conjugate couples of

eigenvalues.

Figure 2. 16 1

st Storey drift time history comparisons

It is observed that the drift response is similar for both specimens during D1 and D2. However, a

major difference observed during D3 is the residual deformations present in Specimen #1. This can be

attributed to the major structural deficiencies that result in significant strength degradation and less

energy dissipation as shown in Figure 2.17. Specimen #2 did not have such an exaggerated residual

displacement. In specimen #1, the sudden failure during D3 in the relatively weaker structure leads to

a larger residual drift.

25

Figure 2. 17 Base shear vs. roof displacement comparison

Table 2. 6 Maximum base shear, roof displacement and 1st storey drift comparisons

Ground

Motion

Max Base Shear

[kN]

Max Roof Displacement

[mm]

Max 1st Storey Drift

[%]

SP1 SP2 SP1 SP2 SP1 SP2

D1 36.6 38.3 9.4 9.3 0.21 0.24

D2 68.5 71.0 48.7 55.1 1.21 1.19

D3 75.1 67.0 206.0 153.2 4.13 4.34

26

Figure 2. 18 1

st mode period time history comparisons

The identified period for Specimen #1 increased from 0.35 seconds at the beginning of D1, to 0.5

seconds at the end of D1, due to cracking. The onset of visible plastic deformations occurred during

D2 and resulted in a period of 0.8 seconds. The period vs. time plot exhibited some oscillations and

spikes which correspond to large plastic behaviour between 10 seconds and 11 seconds. During D3,

the period varied between 0.8 seconds and 1.0 seconds, with the exception of a few spikes between 18

seconds to 20 seconds, reaching a maximum of approximately 2.0 seconds during this range. These

spikes were also affiliated with the extensive damages observed during this time.

In Specimen #2, the period also started at 0.35 seconds and increased to 0.5 seconds towards the end

of D1. One visible difference between the two specimens during D1 is that there is a spike to a period

27

of 0.65 seconds for Specimen #2. One possible explanation is that there was a power outage during

this time, leading to this artificial peak as there were no visible damages during this ground motion.

The pattern observed during D2 was similar to the behaviour of Specimen #1, but the period variation

between 10 seconds and 11 seconds was not as extreme. The peaks of the earthquake did not affect

Specimen #2 as much as Specimen #1.

The largest variations between the two specimens occurred during D3. Extensive damages were

observed for both specimens during D3, but it seems that the peaks of the earthquake once again did

not affect Specimen #2 as much.

Figure 2. 19 Column 101 base and beam 111 left end rotation time history comparisons

Column 101’s base rotation exhibits the same behaviour as the 1st storey drift response, where

Specimen #2’s residual is lesser than that of Specimen #1’s. In the case of Beam 111’s left end

rotation, the residual values are relatively closer to each other, unlike Column 101’s values,

suggesting that the presence lap splices have a bigger influence on column behaviours.

28

29

3. NUMERICAL MODELS

3.1 General

The OpenSees Simulation Platform was used for generating the models (referred to as OS in tables

and figures) of each specimen in order to estimate the seismic response of the test frames. The models

were calibrated through the time history analyses results. The calibrated models were then used in

pushover and time history performance assessments.

Beams and columns in the OpenSees models were modelled using force-based elements defined with

nonlinear fibre sections at integration points. Second order geometric nonlinearity effects were

considered in columns.

Formulation of the Nonlinear Beam Column Element elements follows the Euler-Bernoulli beam

theory, which ignores shear deformations. For the joint regions, joint offsets were made at the element

ends for both beam and column elements in accordance with the procedures defined in ASCE/SEI 41-

06, as the fully rigid joint offsets suggested by TEC 2007 lead to an unreasonably low initial 1st mode

period and did not provide results that matched the global response.

Most column rigid end zones were taken as zero in order to compensate for the effect of joint rotation

on column stiffness as this system was a strong beam-weak column system. Beam lengths were

defined from centerline to centerline of the adjacent columns. Shear deformations at the beam-column

connection regions were neglected in the fibre frame models.

The concrete material model used in the OpenSees models was Concrete01, which is the uniaxial

Kent and Park (1971) concrete material model with no tensile strength and degraded linear

unloading/reloading stiffness as proposed by Karsan and Jirsa (1969). Through this material model,

confinement effects of transverse reinforcement were accounted for by increasing the strength and

strain capacities of the unconfined concrete in order to reflect the behaviour of the concrete in the

confined zones, which have a residual stress associated with them.

For modelling the behavior of steel reinforcement, a stress-strain relation was defined using the

uniaxialMaterial ReinforcingSteel command with 90% of the yield and ultimate strength values of the

reinforcing steel obtained from material tests, to provide more realistic predictions of column

strengths. An onset strain hardening value of 0.01 and an ultimate strain value of 0.1 was used, as

suggested by TEC 2007. The ReinforcingSteel material model was created specifically for simulating

reinforcing steel in a fibre section. A perfect bond between the concrete and steel was assumed in the

models.

Dynamic properties of the specimens were modelled as lumped masses at the nodes with Rayleigh

damping assumed for the time history analyses.

The Static Pushover analysis feature in OpenSees was used to simulate the frame’s nonlinear static

response to the ground motions. The Dynamic Ground-Motion analysis feature in OpenSees was used

to simulate the frame’s nonlinear dynamic response to the ground motions. The Krylov-Newton time-

stepping algorithm was used to better capture any strength degradations.

Figure 3.1 presents an overview of the modelling strategy.

30

Figure 3. 1 OpenSees model with force-based elements

3.2 Specimen #1

The OpenSees models were calibrated with the observed behaviour of Specimen #1 and comparisons

are made between the OpenSees and experimental results. Performance evaluations using these

models were conducted following the procedures defined in TEC 2007 and ASCE/SEI 41-06.

The following global assumptions were made in order to calibrate the model’s time history output to

match the experimental results:

Storeys were modelled as rigid diaphragms;

Column rigid offsets were set as zero, except for the exterior joints at the 1st and 2nd storey, where the full dimension are defined;

Beam rigid offsets were set as the full dimension, except for the exterior joints at the 1st and 2

nd storey, where they were set as zero;

Beam and column longitudinal reinforcement steel behaviour were defined separately;

Concrete strengths at each floor were defined separately;

Steel strengths in columns were 90% of the nominal values determined from the material tests;

The force-based beam and column elements had 5 Gauss-Lobatto integration points;

P-Delta effects were considered in the column elements;

Dead loads were calculated from the weight of steel blocks (which represent the transverse beam and slab weight) and applied as uniformly distributed loads on the beams;

Nodal masses for dynamic analyses were assigned with a dead load factor of 1.0, representative of the physical pseudo-dynamic test; and

The damping value was set at 2.50% for stability purposes (discussed later)

The OpenSees model completes one time history analysis in less than a few minutes on a standard

personal laptop computer and the post-processing for the models are fairly straight forward.

The resulting model for Specimen #1 contained 9 beam elements, 12 column elements, 16 nodes, and

48 degrees of freedom.

3.3 Specimen #1-Comparison with Experimental Results

The OpenSees model time history analysis results for Specimen #1 are presented here in comparison

with the pseudo-dynamic results, as this was used to calibrate the model. The resulting model was

used to conduct pushover and time history analyses for performance evaluations.

The initial 1st mode period from the OpenSees model was 0.48 seconds. The roof displacement time

history comparison is shown in Figure 3.2. The inter-storey drift ratio time history comparisons are

shown in Figure 3.3, and the shear force time history comparisons are shown in Figure 3.4.

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The model does not predict peak displacements well during D1. Even though there are essentially no

residuals in the physical test and the model, the 1st mode period suggests that the model is slightly

stiffer and over-predicted the peak displacements (and forces). As seen in Figure 3.3, none of the 2nd

and 3rd

storey drift residuals are being captured accurately, although some peak values are.

The accuracy of the model was first evaluated through the global responses such as the peak roof

displacement and peak base shear forces obtained during each successive ground motion. Error

percentages for peak roof displacement and peak shear are presented in Table 3.1 and Table 3.2,

respectively. However, the accuracy of numerical models should be evaluated in terms of inter-storey

drift ratios and storey shear forces, as these comparisons capture the effects of higher modes better.

These errors are presented in Table 3.3 and Table 3.4, respectively.

The OpenSees model also did not capture the behaviour during D3 accurately with regards to peaks or

residual displacements. After approximately 18.5 seconds, the damages predicted in the models were

too great and only accumulate in the 1st storey, leading to a soft-storey effect, which was not observed

in the physical test. The specimen appears to have been stronger than expected, as beam mechanism

formations and non-ductile flexural (no shear) failures were observed. Thus, the values in the model

after 18.5 seconds were discarded in the error calculations and comparisons on local scales as they are

not reliable due to the instability experienced in the system. A damping value of 2.50% was arbitrarily

chosen as a value which allows the simulation to run until the very end of D3 ground motion. The

damping value does not significantly affect the results during D1 and D2 ground motions.

It should be noted that extensive damages in the joint regions were observed during D3 for both

specimens, and that a more detailed nonlinear spring element in this region could have been utilized

in the model to better capture damage redistribution. The inability to capture residual drifts in the 2nd

and 3rd

storeys of the model could also be attributed to the fact that the model is only fixed at the 1st

storey column bases, and lacks more detailed elements at the other joints which properly capture

correct rotations. However, this was not done due to time constraints. This joint flexibility could have

been a major factor in the uniform drifts observed in the test specimen as drift capacities are a

function of many factors such as the amount of transverse reinforcement, shear stresses, and axial

loads.

Another reason leading to these inaccurate predictions is the fact that the material models in the

software program were created for simulating “quality” materials. The effects of the accumulated

deficiencies affecting the drift capacities in the specimens were too great and not captured properly.

Modelling materials in deficient systems by using nominal but reduced strength properties in hopes to

predict accurate seismic responses is not very efficient. The main cause is the inability of modelling

degradation during the ground motions. The errors in the model can be generally attributed to

numerical errors.

Figure 3. 2 Roof displacement time history comparison (SP1)

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Figure 3. 3 Inter-storey drift ratio time history comparisons (SP1)

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Figure 3. 4 Storey shear force time history comparisons (SP1)

It is clear that the model captures the storey shear forces better than the inter-storey drifts, indicating

that it is more suitable for force-based assessments. Nonetheless, results of performance evaluations

conducted using strain-based procedures of TEC 2007 and rotation-based procedures of ASCE/SEI

41-06 are presented in the chapter as this was one of the objectives set forth in this thesis study.

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Table 3. 1 Peak roof displacement error (SP1)

Ground Motion Maximum Roof Displacement [mm]

Error [%] Experiment OpenSees

D1 9.14 11.3 23.6

D2 35.6 41.2 15.7

D3 48.3 41.2 -14.7

Table 3. 2 Peak base shear error (SP1)

Ground Motion Maximum Base Shear [kN]

Error [%] Experiment OpenSees

D1 36.5 41.1 12.6

D2 68.5 69.9 2.0

D3 66.6 74.1 11.3

Table 3. 3 Peak inter-storey drift error (SP1)

Storey Ground Motion Maximum Inter-Storey Drift [%]

Error [%] Experiment OpenSees

1st D1 0.20 0.36 80.0

1st D2 1.20 1.64 36.7

1st D3 0.86 1.29 50.0

2nd

D1 0.23 0.35 52.2

2nd

D2 1.28 0.82 -35.9

2nd

D3 1.19 1.04 -12.6

3rd

D1 0.26 0.32 23.1

3rd

D2 1.20 0.60 -50.0

3rd

D3 1.27 0.43 -66.1

Table 3. 4 Peak storey shear error (SP1)

Storey Ground Motion Maximum Storey Shear [kN]

Error [%] Experiment OpenSees

1st D1 36.5 41.1 12.6

1st D2 68.5 69.9 2.0

1st D3 66.6 74.1 11.3

2nd

D1 26.1 33.4 28.0

2nd

D2 47.9 49.8 4.0

2nd

D3 38.2 52.6 37.7

3rd

D1 18.8 28.1 49.5

3rd

D2 41.3 38.2 -7.5

3rd

D3 31.3 24.8 -20.8

As visible in Table 3.3, the 1st storey peak values are over-predicted in the model while the 2

nd and 3

rd

storey values are under-predicted (with the exception of during D1 due to the inability to capture

micro-cracks in the model). Due the formation of a first storey mechanism, the peaks in the 2nd

and 3rd

storeys are not captured as well as the 1st storey. In the 1

st storey, error during D2 is less than those of

D1 (due to energy dissipation) and D3 (due accumulated damages in the 1st storey). Therefore, the

model is more stable and reliable during the intermediate D2 ground motion. As for the peak storey

shear errors presented in Table 3.4, the model mostly over-predicts the values measured from the

experiment, suggesting that full yielding of the steel does not occur during the pseudo-dynamic tests.

Once again, the model results are most reliable in the 1st storey during D2.

35

The curvature time histories of the 1st storey column bases are presented in Figure 3.5, followed by

the column tops in Figure 3.6 as these members are the most critical. It has been shown in the

literature that force-based elements lose objectivity at the local (curvature) and/or global (element)

scale, depending on the number of integration points used. Therefore, objective OpenSees results

obtained using the geometric scaling factors proposed by Coleman and Spacone (2001) are compared

with the experimental results. Up until the point of approximately 18.5 seconds, the analysis results

are in general agreement with the experimental curvature demands. The convention for curvature is

positive in the counter-clockwise direction.

Figure 3. 5 Comparisons of bottom end curvatures of 1

st storey columns (SP1)

36

Figure 3.5 (Continued)

37

Figure 3. 6 Comparisons of top end curvatures of 1

st storey columns (SP1)

38

Peak and residual values during D2 are captured quite well, indicating that the results at the local level

are also reliable. As discussed earlier, the model is unstable during D3 after approximately 18.5

seconds, which is apparent from the over-predicted curvatures at both ends of all members. Another

important observation is that in the experiment, the top residual curvatures are considerably less than

those measured at the bottoms during D3. The OpenSees model does not capture this phenomenon

and predicts the same residual values for the top and bottoms of the elements. Thus, this is another

indication that predictions from the model during D3 are not reliable.

3.4 Specimen #2

Similar to Specimen #1, Specimen #2’s OpenSees model uses force-based elements with the same

material models.

As this specimen had lap splices, separate elements were created in the spliced regions to account for

the extra reinforcement. However, these splice lengths did not conform to the 40db length as required

by TEC 2007 (only 75% of this length was provided). To account for this deficiency, the yield

strength reduction in the model for these spliced-region elements were reduced linearly, as suggested

by TEC 2007 and exponentially, as suggested by ASCE/SEI 41-06.

Dynamic properties of the specimens were modelled as lumped masses at the nodes with a 2.51% (for

TEC 2007) and 2.44% (for ASCE/SEI 41-06) Rayleigh damping assumed for the time history

analyses for stability purposes, as previously discussed.

The resulting model contained 9 beam elements, 24 column elements, 28 nodes, and 84 degrees of

freedom.

The following global assumptions were made as to match, as closely as possible, the calibration of

Specimen #1’s model:

Storeys were modelled as rigid diaphragms;

Column rigid offsets were set as zero, except for the exterior joints at the 1st and 2nd storey, where the full dimension are defined;

Beam rigid offsets were set as the full dimension, except for the exterior joints at the 1st and 2

nd storey, where they were set as zero;

Beam and column longitudinal reinforcement steel behaviour were defined separately;

Concrete strengths at each floor were defined separately;

Steel strengths in columns were 90% of the nominal values determined from the material tests;

The force-based beam and column elements had 5 Gauss-Lobatto integration points and the spliced-region elements had 2 Gauss-Lobatto integration points;

P-Delta effects were considered in the column elements;

Dead loads were calculated from the weight of steel blocks (which represent the transverse beam and slab weight) and applied as uniformly distributed loads on the beams; and

Nodal masses for dynamic analyses were assigned with a dead load factor of 1.0,